ANSWER a The main point is to identify that the one year change in longer term

# Answer a the main point is to identify that the one

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ANSWER a) The main point is to identify that the one-year change in longer-term yields is complementary on the left hand side, and the multi-year return on long term bonds held to one year before maturity is complementary on the right hand side. The graph is good. Time Price Higher 1 year rate in year 1 -2 = lower return of 2 year bond in 0- 1 Time =Higher 1 year rate in 3-4 Lower return of 4 year bond from 0-3 Time Lower return of 4 year bond from 0-1 = Higher 3 year rate in 1-4 ‘safe’ 1 year return b) To really get this right you have to identify the long/short positions. Left side: (3) (1) = (2) (3) (1) = ³ (2) +1 (2) ´ + ³ (2) +1 (3) ´ (1) = 2 ³ (2) +1 (2) ´ +  (2) +1 73 If you run a regression of left and right side on (3) (1) you fi nd that 1 (left) = (right) coe cient of 2 ³ (2) +1 (2) ´ on (3) (1) plus the coe cient of  (2) +1 on (3) (1) . I did not ask for the right side, but here it is. (3) (1) = (2) (3) (1) = (1) +2 + (2) + (1) +2 (3) (1) = (1) +2 (3) + (2) + ³ (1) +2 (1) ´ = ³ (3 1) +2 (2 0) +2 ´ + ³ (1) +2 (1) ´ Corresponding to the two-year change in (1) then is the excess return for buying a 3 year bond and holding for two years, over the return for buying a 2 year bond and holding for 2 years. 12) (15) You form a model of the term structure of interest rates by supposing the one-year rate is an AR(1), (1) +1 = ( (1) ) + +! and that the expectations hypothesis holds. If your model is right, what should the eigenvalue decomposition of forward rates look like? Speci fi cally, if you took data as predicted from your model, (1) (2) (3) and performed Λ 0 =  (  (   0 )) , what would the and Λ look like? Note: you do not have to give the exact values of and Λ . It is enough to answer that columns of have a speci fi c pattern, show where any zeros are, and say what if any parts of or Λ are arbitrary and don’t matter. ANSWER: Forward rates should follow a one-factor model. (2) = ( (1) +1 ) = + ( (1) ) (3) = ( (1) +2 ) = + 2 ( (1) ) ( ) = ( (1) + 1 ) = + 1 ( (1) ) thus Λ will have only one non-zero element Λ = 1 0 0 0 0 0 0 0 0 and will look like = 1 | | 2 3 2 | | where is an arbitrary constant — the pattern is 1    2 . Since they multiply zeros, the second and third columns of are irrelevant .  • • • 